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Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces

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  • Singh, Ajeet
  • Shukla, Anurag
  • Vijayakumar, V.
  • Udhayakumar, R.

Abstract

In this article, we discuss the asymptotic stability and mean square stability of stochastic differential equations of fractional-order 1<α≤2. We have considered the family of stochastic differential equations with variable delay in the state. For proving our main results, we apply the Banach fixed point theorem and imposed the Lipschitz condition on nonlinearity. Finally, we present an example to illustrate the obtained theory.

Suggested Citation

  • Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004495
    DOI: 10.1016/j.chaos.2021.111095
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    References listed on IDEAS

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    1. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, February.
    3. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    4. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "A new approach on approximate controllability of fractional evolution inclusions of order 1 < r < 2 with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
    6. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
    7. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R. & Zhou, Yong, 2020. "A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Y. Ren & D. D. Sun, 2010. "Second-order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 569-582, December.
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    8. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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